Analysis of a bulk queue with unreliable server, immediate feedback, N-policy, Bernoulli schedule multiple vacation and stand-by server

We have studied the behaviour of a non-Markovian bulk service queueing model with unreliable server, stand-by server, loss and feedback, N-policy and Bernoulli schedule multiple vacation. The stand-by server is employed only during the main server's repair period. At each service completion the main server may have an option to go for a short vacation. After each short vacation completion or service completion, if the system size is less than 'a', the server takes a sequence of vacation until the queue size reaches at least 'N'. The concept of loss and feedback is also incorporated in this model. The PGF of queue size and some important performance measures are derived. An extensive numerical result is illustrated. (C) 2019 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Ain Shams University.